A New Mathematical Model for Evolutionary Games on Finite Networks of Players

A new mathematical model for evolutionary games on graphs is proposed to extend the classical replicator equation to finite populations of players organized on a network with generic topology. Classical results from game theory, evolutionary game theory and graph theory are used. More specifically, each player is placed in a vertex of the graph and he is seen as an infinite population of replicators which replicate within the vertex. At each time instant, a game is played by two replicators belonging to different connected vertices, and the outcome of the game influences their ability of producing offspring. Then, the behavior of a vertex player is determined by the distribution of strategies used by the internal replicators. Under suitable hypotheses, the proposed model is equivalent to the classical replicator equation. Extended simulations are performed to show the dynamical behavior of the solutions and the potentialities of the developed model.Comment: 26 pages, 7 figures, 1 tabl

Cue-Triggered Addiction and Natural Recovery

In this paper we propose a model of natural recovery, a widespread yet unexplained aspect of addictive behavior, starting from the recent theory developed by Bernheim and Rangel (2004). While the Bernheim and Rangel model generates many distinctive patterns of addiction, it does not explicitly consider pathways to natural recovery. Based on insights from neurosciences, we introduce an ”implicit cognitive appraisal” process depending on past experiences as well as on future expected consequences of addictive consumption. Such function affects the individual in two ways: it erodes the payoff from use as the decision maker grows older and it increases the cognitive control competing with the hedonic impulses to use, thus reducing the probability of making mistakes. While we do recognize the importance of allowing for cue-triggered mistakes in individual decision making, our model recovers an important role for cognitive processes, such as subjective cost-benefit evaluations, in explaining natural recovery.Addiction models, natural recovery, behavioral economics,cognitive policy, neuroscience.

Self-regulation versus social influence for promoting cooperation on networks

Cooperation is a relevant and controversial phenomenon in human societies. Indeed, although it is widely recognized essential for tackling social dilemmas, finding suitable policies for promoting cooperation can be arduous and expensive. More often, it is driven by pre-established schemas based on norms and punishments. To overcome this paradigm, we highlight the interplay between the influence of social interactions on networks and spontaneous self-regulating mechanisms on individuals behavior. We show that the presence of these mechanisms in a prisoner’s dilemma game, may oppose the willingness of individuals to defect, thus allowing them to behave cooperatively, while interacting with others and taking conflicting decisions over time. These results are obtained by extending the Evolutionary Game Equations over Networks to account for self-regulating mechanisms. Specifically, we prove that players may partially or fully cooperate whether self-regulating mechanisms are sufficiently stronger than social pressure. The proposed model can explain unconditional cooperation (strong self-regulation) and unconditional defection (weak self-regulation). For intermediate selfregulation values, more complex behaviors are observed, such as mutual defection, recruiting (cooperate if others cooperate), exploitation of cooperators (defect if others cooperate) and altruism (cooperate if others defect). These phenomena result from dynamical transitions among different game structures, according to changes of system parameters and cooperation of neighboring players. Interestingly, we show that the topology of the network of connections among players is crucial when self-regulation, and the associated costs, are reasonably low. In particular, a population organized on a random network with a Scale-Free distribution of connections is more cooperative than on a network with an Erdös-Rényi distribution, and, in turn, with a regular one. These results highlight that social diversity, encoded within heterogeneous networks, is more effective for promoting cooperation

A Model of Spontaneous Remission from Addiction

This article develops a formal model of spontaneous recovery from pathological addiction. It regards addiction as a progressive susceptibility to stochastic environmental cues and introduce a cognitive appraisal process in individual decision making depending on past addiction experiences and on their future expected consequences. This process affects consumption choices in two ways. The reward from use decreases with age. At the same time, cognitive incentives emerge that reduce the probability of making mistakes. In addition to modeling the role of cue-triggered mistakes in individual decision making, the analysis highlights the role of other factors such as subjective self-evaluation and cognitive control. The implications for social policy and for the treatment of drug and alcohol dependence are discussed

A machine learning approach to assess Sustainable Development Goals food performances: The Italian case

In this study, we introduce an innovative application of clustering algorithms to assess and appraise Italy's alignment with respect to the Sustainable Development Goals (SDGs), focusing on those related to climate change and the agrifood market. Specifically, we examined SDG 02: Zero Hunger, SDG 12: Responsible Consumption and Production, and SDG 13: Climate Change, to evaluate Italy's performance in one of its most critical economic sectors. Beyond performance analysis, we administered a questionnaire to a cross-section of the Italian populace to gain deeper insights into their awareness of sustainability in everyday grocery shopping and their understanding of SDGs. Furthermore, we employed an unsupervised machine learning approach in our research to conduct a comprehensive evaluation of SDGs across European countries and position Italy relative to the others. Additionally, we conducted a detailed analysis of the responses to a newly designed questionnaire to gain a reasonable description of the population's perspective on the research topic. A general poor performance in the SDGs indicators emerged for Italy. However, from the questionnaire results, an overall significant interest in the sustainability of the acquired products from italian citizens

A multi-modal machine learning approach to detect extreme rainfall events in Sicily

In 2021 almost 300 mm of rain, nearly half of the average annual rainfall, fell near Catania (Sicily Island, Italy). Such events took place in just a few hours, with dramatic consequences on the environmental, social, economic, and health systems of the region. These phenomena are now very common in various countries all around the world: this is the reason why, detecting local extreme rainfall events is a crucial prerequisite for planning actions, able to reverse possibly intensified dramatic future scenarios. In this paper, the Affinity Propagation algorithm, a clustering algorithm grounded on machine learning, was applied, to the best of our knowledge, for the first time, to detect extreme rainfall areas in Sicily. This was possible by using a high-frequency, large dataset we collected, ranging from 2009 to 2021 which we named RSE (the Rainfall Sicily Extreme dataset). Weather indicators were then been employed to validate the results, thus confirming the presence of recent anomalous rainfall events in eastern Sicily. We believe that easy-to-use and multi-modal data science techniques, such as the one proposed in this study, could give rise to significant improvements in policy-making for successfully contrasting climate change

Nonlinear behavior of coupled Evolutionary Games -- Epidemiological Models

Epidemiological models are an important tool in coping with epidemics, as they offer a forecast, even if often simplistic, of the behavior of the disease in the population. This allows responsible health agencies to organize themselves and adopt strategies to minimize and postpone the population's infection peaks. While during an epidemic outbreak, the available model can be used to describe the behavior of the disease in order to aim for fast and efficient forecasts of the epidemiological scenario, once the epidemiological emergency is over, the objective of the subsequent works is to extend models by integrating new facts and information, thus providing more efficient tools to face future epidemics. In this sense, we present an epidemiological model that takes into account on one hand, the creation of a vaccine during an epidemic outbreak (as we saw happen in the case of COVID-19) and that, on the other hand, considers the impact of the cooperative behavioral choices of individuals.Comment: 19 pages, 5 figure